Early Detection of Emergent Events Based on an Extremal Process Approach

2000 Mathematics Subject Classification: Primary 60G70, 62F03.

We explore a real renewal process representing the successive arrival times of some event (ex.: clinical case of an infectious disease). We wish to test that the first observed events are sporadic, and not emergent. We also compare this distribution to the one got under the independency of standard setting. We finally illustrate this approach by testing on the first observations of a simulation of a slowly emergent phenomenon that this phenomenon is a sporadic one, and we show that the statistic based on the extremal process is much more efficient and robust than the statistic based on the record values.